Question

7x+3y=−25

−7x+9y=−47

Answer 1

To solve this system of linear equations, we can use the method of elimination. Let's multiply the first equation by 7 and the second equation by 1 to make the x coefficients opposites:

7(7x + 3y) = 7(-25)
-7x + 9y = -47

This gives us:

49x + 21y = -175
-7x + 9y = -47

Now, let's add these two equations together to eliminate the x variable:

49x + 21y - 7x + 9y = -175 - 47
42x + 30y = -222

Dividing through by 6:

7x + 5y = -37

Now, let's take this equation and the second original equation and solve the system.

7x + 5y = -37
-7x + 9y = -47

Adding these two equations together to eliminate x:

14y = -84
y = -6

Now, substitute y = -6 into the second original equation to solve for x:

-7x + 9(-6) = -47
-7x - 54 = -47
-7x = 7
x = -1

Therefore, the solution to the system of equations is x = -1 and y = -6.